This is a neural network in python built using only numpy and similar basic libraries. Formulas (derivatives) for backpropogation are provided in the comments. We first train on one observation at a time, and then see improved training using minibatches. Using minibatches we get better accuracy with the same size training data, and we can see that the network is learning digit shapes in plots of the weights. This notebook is focused on being readable. Our network is trained and tested on the classic MINST digits dataset (http://yann.lecun.com/exdb/mnist/).